I have to estimate an autoregression in a general form: X(t)=a+ b*X(t-1) + dummy + e(t). The dummy variable takes 1 for only one observation and zero elsewhere. My question is: can I estimate the model above, obtain the estimate od the dummy variable, calculate Z(t) =X(t)-estimated dummy (so effectivelly I subtract the estimated value of dummy from one observation in X) and then estimate the model as: Z(t) = c + b1*Z(t-1) + n(t)?
I will appreciate any answer or link to literature,
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